Suppose that you want to test the hypothesis that a coin has...

Suppose that you want to test the hypothesis that a coin has a probability of $1 / 2$ of coming up heads when you flip it. You flip it 5 times and it comes up heads every time. How likely is it that you would see a pattern of 5 heads in a row if true probability of coming up heads is $1 / 2 ?$

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Key Concepts

Hypothesis Testing

A statistical procedure used to determine whether there is enough evidence in a sample of data to infer that a certain claim about a population parameter is true. In this context, it involves assessing whether the observed sequence of coin flips is consistent with the coin being fair.

Statistical Significance

This concept refers to the determination of whether an observed effect or pattern is unlikely to have occurred by chance alone. It is crucial when evaluating whether the result of 5 consecutive heads provides sufficient evidence to challenge the hypothesis of a fair coin.

Binomial Distribution

This is a probability distribution that models the number of successes in a fixed number of independent trials, each with the same probability of success. It is relevant to calculating the likelihood of outcomes such as getting 5 heads in 5 coin flips.

Probability Theory

This concept provides the mathematical framework for quantifying the likelihood of events occurring under uncertainty. It is key to understanding how to model situations like coin flips by assigning probabilities to potential outcomes.

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